Create an edge between a "real" and an array modifier vertex?
Scenario 1

Make one copy of Array real to be able snap extruded vertex and add Array modifier again. Like:


Duplicate Array modifier (and disable one of them)
Set Count 2 and Apply
Enable Snap > Vertex type
Create connection by Extruding E Vertex
Delete unwanted parts (second teeth)
Enable Array modifier back


Scenario 2

Do it out of edit mode by another object and than join them. Like ...


in Edit mode Shift+D first vertex
Separate > Selected P
in Object mode select separeted vertex, go to edit mode
enable Snap tool and to Vertex
select vertex, Extrude E, Snap to first Array copy
go to Object mode and Join these two Objects Ctrl+J


BTW Do you know there is a addon GearGenMaster?